Related papers: Estimation of mutual information via quantum kerne…

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…

Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…

The abundance of training data is not guaranteed in various supervised learning applications. One of these situations is the post-earthquake regional damage assessment of buildings. Querying the damage label of each building requires a…

Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…

We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning models. To accurately estimate MI from a finite number of samples, we present GMM-MI…

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available…

Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…

With the success of self-supervised representations, researchers seek a better understanding of the information encapsulated within a representation. Among various interpretability methods, we focus on classification-based linear probing.…

A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum…

We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to…

The main objective of the Multiple Kernel k-Means (MKKM) algorithm is to extract non-linear information and achieve optimal clustering by optimizing base kernel matrices. Current methods enhance information diversity and reduce redundancy…

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…

We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test…

Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…

The ability to compress observational data and accurately estimate physical parameters relies heavily on informative summary statistics. In this paper, we introduce the use of mutual information (MI) as a means of evaluating the quality of…

Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…

In models of opinion dynamics, many parameters -- either in the form of constants or in the form of functions -- play a critical role in describing, calibrating, and forecasting how opinions change with time. When examining a model of…

We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…

Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both…